The Variation of Isometric Energy Rates With Muscle Length: A Distribution-Moment Model Analysis

1992 ◽  
Vol 114 (4) ◽  
pp. 542-546 ◽  
Author(s):  
E. Rouhaud ◽  
G. I. Zahalak
Keyword(s):  
Heat Production ◽  
Isometric Force ◽  
Muscle Length ◽  
Simple Relation ◽  
Isometric Tension ◽  
Model Parameters ◽  
A Value ◽  
Muscle Dynamics ◽  
Dimensionless Constant ◽  
Distribution Moment

The Distribution-Moment Model of skeletal muscle, which has been enhanced recently to make possible the calculation of chemical energy release (E˙) and heat production (H˙) rates [1], is applied to isometric muscle. Under steady-state isometric conditions the model predicts a simple relation between the energy rates and the muscle length, namely (E/˙E˙max)=(H/˙H˙max)=[1+Bα(Λ)]/[1+B], where Λ is the ratio of muscle length to the “optimal” length at which maximal isometric tension is produced, and α(Λ) is a function numerically equal to the ratio of the tetanic isometric force to its maximum value. The single dimensionless constant in this relation, B, can be calculated from model parameters characterizing muscle dynamics at the optimum length, and has a value near unity for frog sartorius at 0°C. The predicted behavior is shown to agree reasonably well with experimental measurements of heat production and phosphocreatine (PCr) hydrolysis. The model relates the isometric energy rates to PCr hydrolysis in (1) cross-bridge interactions, and (2) calcium pumping into the sarcoplasmic reticulum.

The energetic cost of activation of white muscle fibres from the dogfish Scyliorhinus canicula

1997 ◽  
Vol 200 (3) ◽  
pp. 495-501 ◽  
Author(s):  
F Lou ◽  
N Curtin ◽  
R Woledge
Keyword(s):  
Heat Production ◽  
White Muscle ◽  
Isometric Force ◽  
Force Production ◽  
Total Heat ◽  
Energetic Cost ◽  
Maximum Efficiency ◽  
Muscle Fibres ◽  
Scyliorhinus Canicula ◽  
A Value

The energetic cost of activation was measured during an isometric tetanus of white muscle fibres from the dogfish Scyliorhinus canicula. The total heat production by the fibres was taken as a measure of the total energetic cost. This energy consists of two parts. One is due to crossbridge interaction which produces isometric force, and this part varies linearly with the degree of filament overlap in the fibres. The other part of the energy is that associated with activation of the crossbridges by Ca2+, mainly with uptake of Ca2+ into the sarcoplasmic reticulum by the ATP-driven Ca2+ pump. Total heat production was measured at various degrees of filament overlap beyond the optimum for force development. Extrapolation of heat versus force production data to evaluate the heat remaining at zero force gave a value of 34±5 % (mean ± s.e.m., N=24) for activation heat as a percentage of total heat production in a 2.0 s isometric tetanus. Values for 0.4 and 1.0 s of stimulation were similar. Comparison with values in the literature shows that the energetic cost of activation in dogfish muscle is very similar to that of frog skeletal muscle and it cannot explain the lower maximum efficiency of dogfish muscle compared with frog muscle. The proportion of energy for activation (Ca2+ turnover) is similar to that expected from a simple model in which Ca2+ turnover was varied to minimize the total energy cost for a contraction plus relaxation cycle.

Calcium effects on contractility and heat production in mammalian myocardium

1986 ◽  
Vol 251 (1) ◽  
pp. H127-H132 ◽  
Author(s):  
J. E. Ponce-Hornos ◽  
A. C. Taquini
Keyword(s):  
Papillary Muscle ◽  
Heat Production ◽  
Muscle Length ◽  
Heat Rate ◽  
Isometric Tension ◽  
Tension Development ◽  
Contractile System ◽  
Dimensionless Ratio ◽  
Calcium Effects ◽  
Mammalian Myocardium

The effects of changing external Ca concentration ([Ca]o) on contractile parameters and heat production were investigated in the interventricular rabbit septa and the dog papillary muscle. Double reciprocal plots of tension development as a function of [Ca]o yielded half-maximal activation values of 1.04 +/- 0.17 and 2.8 +/- 0.7 mM Ca for the septum and papillary muscle, respectively. Resting heat rate was similar in both preparations, 1.9 +/- 0.08 mW . g-1 for the septum and 1.7 +/- 0.07 mW . g-1 for the papillary muscle, and it was not altered by changes in [Ca]o. Active heat production (Ha) normalized per unit of force developed (19 +/- 1.3 microJ . mN-1 . g-1) for the septum and the dimensionless ratio Ha/(To . lo), (0.30 +/- 0.02) for the papillary muscle, where To is the isometric tension and lo, the muscle length, remained unaltered with changes in [Ca]o. Total heat production per beat normalized per unit of force developed (Ht/T) for the septum and the ratio Ht/(To . lo) for the papillary muscle decreased hyperbolically with [Ca]o. Therefore, as a result of the unaltered economy of the contractile system and the unchanged resting heat rate, muscle economy improves as [Ca]o approaches physiological levels. Further increase in [Ca]o, over the physiological levels, can only slightly improve muscle economy.

Maximum Air Suction Into a Louvered Funnel Through Optimum Design

2012 ◽  
Vol 56 (01) ◽  
pp. 1-11 ◽  
Author(s):  
Dipti P. Mishra ◽  
Sukanta K. Dash
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Numerical Experiments ◽  
Simple Relation ◽  
Maximum Amount ◽  
Fluid Temperature ◽  
Entrance Length ◽  
A Value ◽  
Suction Rate ◽  
Flow Case

The rate of air suction into a louvered cylindrical funnel with lateral openings has been computed numerically by solving the equations of conservation of mass, momentum, and energy along with the two k-z turbulence closure equations. It was found that the air suction rate into a louvered funnel can be maximum for an optimum nozzle protrusion length into the funnel irrespective of the nozzle fluid temperature. There also exists an optimum funnel diameter (irrespective of the nozzle fluid temperature) and funnel height for which the air suction rate can be the maximum. Keeping the volume of the funnel constant, the shape of the funnel was changed to a frustum. It was found that an inverted frustum with a value of r1/r2 = 0.8 could suck the maximum amount of air compared to a cylindrical funnel of the same volume. The cylindrical sucking funnel has interestingly a much shorter entrance length compared to a simple pipe flow case with the same entrance Reynolds number. The entrance length for the sucking funnel is also a function of the nozzle fluid temperature, and a simple relation for the entrance length as a function of Ren and Tn/T∞ could also be developed for a sucking funnel. Numerical experiments were done for an inclined funnel to compute the mass suction into it. It was found that for Gr/Re2 ≤ 0.4 (where Gr is the Grashof number and Re is the Reynolds number) given by the funnel inclination had no effect on the rate of mass suction while for 0.4 < Gr/Re2 < 1 the funnel inclination had marginal influence. As the value of Gr/Re2 increased beyond 1 the influence of the funnel inclination on rate of mass suction was found to be significant.

Device Modeling of a-Si:H Alloy Solar Cells: Calibration Procedure for Determination of Model Input Parameters

1998 ◽  
Vol 507 ◽  
Author(s):  
M. Zeman ◽  
R.A.C.M.M. Van Swaaij ◽  
E. Schroten ◽  
L.L.A. Vosteen ◽  
J.W. Metselaar
Keyword(s):  
Solar Cell ◽  
Material Properties ◽  
Calibration Procedure ◽  
Model Parameters ◽  
Model Input ◽  
A Value ◽  
Input Parameters ◽  
Simulated Material ◽  
Good Agreement

ABSTRACTA calibration procedure for determining the model input parameters of standard a-Si:H layers, which comprise a single junction a-Si:H solar cell, is presented. The calibration procedure consists of: i) deposition of the separate layers, ii) measurement of the material properties, iii) fitting the model parameters to match the measured properties, iv) simulation of test devices and comparison with experimental results. The inverse modeling procedure was used to extract values of the most influential model parameters by fitting the simulated material properties to the measured ones. In case of doped layers the extracted values of the characteristic energies of exponentially decaying tail states are much higher than the values reported in literature. Using the extracted values of model parameters a good agreement between the measured and calculated characteristics of a reference solar cell was reached. The presented procedure could not solve directly an important issue concerning a value of the mobility gap in a-Si:H alloys.

scholarly journals Influence of muscle length on work from trabecular muscle of frog atrium and ventricle.

1995 ◽  
Vol 198 (10) ◽  
pp. 2221-2227 ◽  
Author(s):  
D A Syme ◽  
R K Josephson
Keyword(s):  
Isometric Force ◽  
Muscle Length ◽  
Work Capacity ◽  
Linear Increase ◽  
Ventricular Muscle ◽  
Work Output ◽  
Loop Technique ◽  
Work Done ◽  
The Relationship ◽  
Work Loop

The work capacity of segments of atrial and ventricular muscle from the frog Rana pipiens was measured as a function of muscle length using the work loop technique. Both the work done during shortening and the work required to re-lengthen the muscle after shortening increased with muscle length. Net work increased with length up to a maximum, beyond which work declined. The optimum sarcomere length for work output was 2.5-2.6 microns for both atrial and ventricular muscle. Isometric force increased with muscle length to lengths well beyond the optimum for work output. Thus, the decline in work at long lengths is not simply a consequence of a reduction in the capacity of heart muscle to generate force. It is proposed that it is the non-linear increase in work required to re-lengthen muscle with increasing muscle length which limits net work output and leads to a maximum in the relationship between net work and muscle length. Extension of the results from muscle strips to intact hearts suggests that the work required to fill the ventricle exceeds that available from atrial muscle at all but rather short ventricular muscle lengths.

A bladder contractility constant

1983 ◽  
Vol 245 (5) ◽  
pp. R673-R677
Author(s):  
J. C. Byrne ◽  
A. Tozeren
Keyword(s):  
Initial Velocity ◽  
Active Component ◽  
Isometric Force ◽  
Muscle Length ◽  
Rate Of Change ◽  
Contractile Element ◽  
Tetanic Contraction ◽  
Muscle Contractility ◽  
Maximum Isometric Force ◽  
The Moment

Muscle contractility can be characterized by two related properties: force and velocity. The initial velocity of a tetanic contraction is inversely related to preload. This was demonstrated experimentally by Hill and quantified in his well-known empiric equation. Subsequent investigators argued that a theoretical maximum contractile element velocity (V max) could be predicted from the rate of change of isometric force. V max has been applied clinically in heart studies, prompting others to use similar methods to evaluate bladder contractility. These attempts have so far been unsuccessful. The present study shows for whole canine bladders that the time to reach maximum isometric force from the moment of onset of active contraction is a constant independent of muscle length, preload, and maximum force. This can be expressed as a frequency constant (omega) whose calculation appears similar to that for V max. In contrast to V max, omega is obtained only from the active component of pressure.

Muscle shortening increases sensitivity of fatigue to severe hypoxia in canine diaphragm

1991 ◽  
Vol 71 (6) ◽  
pp. 2309-2316 ◽  
Author(s):  
B. T. Ameredes ◽  
M. W. Julian ◽  
T. L. Clanton
Keyword(s):  
Flow Characteristics ◽  
Muscle Length ◽  
Isometric Tension ◽  
Severe Hypoxia ◽  
Mean Power ◽  
Tension Development ◽  
Moderate Hypoxia ◽  
O2 Supply ◽  
Mean Power Output

The effects of inspired O2 on diaphragm tension development during fatigue were assessed using isovelocity (n = 6) and isometric (n = 6) muscle contractions performed during a series of exposures to moderate hypoxia [fraction of inspired O2 (FIO2) = 0.13], hyperoxia (FIO2 = 1), and severe hypoxia (FIO2 = 0.09). Muscle strips were created in situ from the canine diaphragm, attached to a linear ergometer, and electrically stimulated (30 Hz) to contract (contraction = 1.5 s/relaxation = 2 s) from optimal muscle length (Lo = 8.9 cm). Isovelocity contractions shortened to 0.70 Lo, resulting in a mean power output of 210 mW/cm2. Fatigue trials of 35 min duration were performed while inspired O2 was sequentially changed between the experimental mixtures and normoxia (FIO2 = 0.21) for 5-min periods. In this series, severe hypoxia consistently decreased isovelocity tension development by an average of 0.1 kg/cm2 (P less than 0.05), which was followed by a recovery of tension (P less than 0.05) on return to normoxia. These responses were not consistently observed in isometric trials. Neither isovelocity nor isometric tension development was influenced by moderate hypoxia or hyperoxia. These results demonstrate that the in situ diaphragm is relatively insensitive to rapid changes in O2 supply over a broad range and that the tension development of the shortening diaphragm appears to be more susceptible to severe hypoxia during fatigue. This may reflect a difference in either the metabolic or blood flow characteristics of shortening contractions of the diaphragm.

Isotonic relaxation in cardiac muscle

1975 ◽  
Vol 229 (3) ◽  
pp. 646-651 ◽  
Author(s):  
JE Strobeck ◽  
AS Bahler ◽  
EH Sonnenblick
Keyword(s):  
Cardiac Muscle ◽  
Isometric Force ◽  
Muscle Length ◽  
Constant Load ◽  
Papillary Muscles ◽  
Initial Length ◽  
Total Load ◽  
Relaxation Velocity ◽  
Force Velocity ◽  
Maximum Isometric Force

The force-velocity-length determinants of isotonic relaxation were studied in 12 cat papillary muscles. Isotonic relaxation velocity (VL) was found to be a function of total load (preload + afterload), with peak VL increasing to a maximum at loads approximately .3 to .4 Po(L') (Po(L') defined as maximum isometric force developed during a twitch at the experimental length) and falling with increasing loads. Initial muscle length (ML) had no effect on the peak VL with constant load. Increasing the initial length at which isotonic relaxation occurred (LL) decreased peak VL but did not alter the unique length-velocity trajectory at constant load. This unique length-velocity trajectory occurred, despite a wide variation in time during the contraction when peak VL was measured. Increasing Ca++ from 2.5 to 7.5 mM increased peak VL (1.73 +/- .16 to 2.32 +/- .20 ML/s) and shifted the entire length-velocity trajectory toward higher velocities of lengthening. The addition of 10 mM caffeine increased peak VL also (1.67 +/- .18 to 2.54 +/- .20 ML/s) and had a similar effect on the length-velocity trajectory during lengthening as Ca++. Both increased Ca++ and caffeine (10 mM) augmented the maximum VL measured on addition of load.

scholarly journals Effect of an ADP analog on isometric force and ATPase activity of active muscle fibers

2003 ◽  
Vol 284 (4) ◽  
pp. C816-C825 ◽  
Author(s):  
Christina Karatzaferi ◽  
Kathryn H. Myburgh ◽  
Marc K. Chinn ◽  
Kathleen Franks-Skiba ◽  
Roger Cooke
Keyword(s):  
Creatine Kinase ◽  
Simple Model ◽  
Atpase Activity ◽  
Isometric Force ◽  
Psoas Muscle ◽  
Isometric Tension ◽  
Active Muscle ◽  
Absolute Value ◽  
Cross Bridge ◽  
Skinned Muscle

The role played by ADP in modulating cross-bridge function has been difficult to study, because it is hard to buffer ADP concentration in skinned muscle preparations. To solve this, we used an analog of ADP, spin-labeled ADP (SL-ADP). SL-ADP binds tightly to myosin but is a very poor substrate for creatine kinase or pyruvate kinase. Thus ATP can be regenerated, allowing well-defined concentrations of both ATP and SL-ADP. We measured isometric ATPase rate and isometric tension as a function of both [SL-ADP], 0.1–2 mM, and [ATP], 0.05–0.5 mM, in skinned rabbit psoas muscle, simulating fresh or fatigued states. Saturating levels of SL-ADP increased isometric tension (by P′), the absolute value of P′ being nearly constant, ∼0.04 N/mm2, in variable ATP levels, pH 7. Tension decreased (50–60%) at pH 6, but upon addition of SL-ADP, P′ was still ∼0.04 N/mm2. The ATPase was inhibited competitively by SL-ADP with an inhibition constant, K i, of ∼240 and 280 μM at pH 7 and 6, respectively. Isometric force and ATPase activity could both be fit by a simple model of cross-bridge kinetics.

Sign in / Sign up

Export Citation Format

Share Document